Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem C. 1354. (April 2016)

C. 1354. In a circle of unit radius, $\displaystyle n$ identical small circles ($\displaystyle n>2$) are drawn such that each of them touches the unit circle on the inside, and also touches both of the adjacent small circles. What fraction of the area of the unit circle is covered by the small circles? For $\displaystyle n=3$, 4 and 6, calculate the numerical value of the ratio.

(5 pont)

Deadline expired on May 10, 2016.

### Statistics:

 96 students sent a solution. 5 points: Cseh Noémi, Csorba Benjámin, Édes Lili, Fajszi Bulcsú, Fekete Balázs Attila, Geretovszky Anna, Horcsin Tamás, Horváth András János, Kasó Ferenc, Kis 999 Alexandra, Komoróczy Ádám, Kormányos Hanna Rebeka, Kovács-Deák Zsombor, Lévay Mátyás, Marozsák Tóbiás , Matusek Márton, Molnár 410 István, Nagy 911 Viktória, Nagy Marcell, Nagy Viktor, Németh Csilla Márta, Páhoki Tamás, Póta Balázs, Pszota Máté, Richlik Róbert, Sebe Anna, Simon Ákos, Sudár Ákos, Szauer Marcell, Szécsényi Júlia, Szilágyi Éva, Tatai Mihály, Tóth 111 Máté , Török Réka , Tubak Dániel, Weisz Máté, Zsombó István. 4 points: Garamvölgyi István Attila, János Zsuzsa Anna, Mályusz Attila, Sal Dávid. 3 points: 29 students. 2 points: 13 students. 1 point: 9 students. 0 point: 4 students.

Problems in Mathematics of KöMaL, April 2016